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Year 9

Checking and securing understanding of multiples of 10

I can factorise multiples of 10^n in order to simplify multiplication and division of both integers and decimals.

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New
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Year 9

Checking and securing understanding of multiples of 10

I can factorise multiples of 10^n in order to simplify multiplication and division of both integers and decimals.

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Lesson details

Key learning points

  1. Factorising multiples of 10 can scale the calculation to easier values.
  2. It is important to consider place value so answers are scaled back correctly when multiplying.
  3. Equivalent fractions can be used to simplify division.

Keywords

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

  • Commutative - An operation is commutative if the values it is operating on can be written in either order without changing the calculation.

Common misconception

There are many ways to multiply decimals or large numbers. With decimals, some pupils choose to multiply decimals using the column method and incorrectly use a decimal point when calculating answers.

When multiplying decimals, converting the calculation using integers and powers of 10 makes the calculation easier to work with.

To embed the understanding of powers of 10, quick fire questions on MWB can be given where answers must have a multiplication of 1/10 or 1/100 etc. Pupils see the variety of ways a calculation can be written. E.g. 2.3 x 0.4 = (23x4)/100 = 92/100 = (23x4)/10^2 = 92/100 = 92/10^2
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
When a number is multiplied by itself multiple times, it can be written more simply in __________ form.
Correct answer: exponential
fractional
irregular
regular
Q2.
Fill in the missing exponent of $$8\times8\times8\times8\times8 = 8^\square$$
$$2$$
$$3$$
$$4$$
Correct answer: $$5$$
$$8$$
Q3.
Match each missing exponent with the correct statement.
Correct Answer:$$7$$,$$8\times8\times8\times8\times8\times8\times8 = 8^\square$$

$$8\times8\times8\times8\times8\times8\times8 = 8^\square$$

Correct Answer:$$8$$,$$4\times4\times4\times4\times4\times4\times4\times4= 4^\square$$

$$4\times4\times4\times4\times4\times4\times4\times4= 4^\square$$

Correct Answer:$$5$$,$$5\times5\times5\times5\times5= 5^\square$$

$$5\times5\times5\times5\times5= 5^\square$$

Correct Answer:$$2$$,$$100 = 10^\square$$

$$100 = 10^\square$$

Correct Answer:$$4$$,$$10000 = 10^\square$$

$$10000 = 10^\square$$

Correct Answer:$$1$$,$$10 = 10^\square$$

$$10 = 10^\square$$

Q4.
Which of the following equate to 240?
Correct answer: 24 × 10
Correct answer: 8 × 3 × 10
Correct answer: 3 × 4 × 2 × 10
3 × 4 × 20 × 10
Correct answer: 6 × 2 × 20
Q5.
Match each number written in exponent form with its value.
Correct Answer:$$10^4$$,$$10 000$$

$$10 000$$

Correct Answer:$$10^2$$,$$100$$

$$100$$

Correct Answer:$${1} \over {10^2}$$ ,$$0.01$$

$$0.01$$

Correct Answer:$$10^0$$,$$1$$

$$1$$

Correct Answer:$$10^6$$,$$1 000 000$$

$$1 000 000$$

Correct Answer:$${1} \over {10^3}$$ ,$$0.001$$

$$0.001$$

Q6.
Without a calculator, work out 3.4 × 1.5.
Correct Answer: 5.1, 5.10

Exit quiz

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6 Questions

Q1.
Using the Gattegno chart or otherwise, work out which of the following calculations equate to 24.
An image in a quiz
Correct answer: 3 × 8
Correct answer: 30 × 0.8
Correct answer: 4 × 6
Correct answer: 0.4 × 60
4 × 60
Q2.
Using the Gattegno chart or otherwise, match each calculation to its correct answer.
An image in a quiz
Correct Answer:2 × 3 = 0.2 × 30 = 0.3 × 20,6

6

Correct Answer:4 × 2 = 0.4 × 20 = 0.2 × 40,8

8

Correct Answer:0.7 × 20 = 0.2 × 70 = 7 × 2,14

14

Correct Answer:0.3 × 30 = 3 × 3 = 0.03 × 300,9

9

Q3.
Using the associative law to partition 4000 and 2000 into powers of 10, find the calculations that are equivalent to 4000 × 2000.
Correct answer: $$4 \times 2 \times 1000 \times 1000$$
Correct answer: $$8\times 10^6$$
$$4\times2\times 100\times 100$$
$$4\times2\times 10000\times 1000$$
$$4\times10000\times2\times1000$$
Q4.
Which of the following calculations are equivalent to $$5000\times5000$$?
Correct answer: $$5\times1000\times5\times1000$$
Correct answer: $$25\times 10^6$$
Correct answer: $$2.5\times 10^7$$
$$2.5\times 10^6$$
$$25\times 10^7$$
Q5.
Which of the following calculations are equivalent to $$6.5\times2.4$$?
Correct answer: $$65\times24\times\frac{1}{100}$$
$$\frac{6.5\times2.4}{100}$$
Correct answer: $$65\times24\times\frac{1}{10^2}$$
Correct answer: $$\frac{65\times24}{100}$$
$$\frac{6.5\times2.4}{10^2}$$
Q6.
Which of the following calculations are equivalent to $$4.5\times0.03$$?
$$\frac{45\times3}{10^2}$$
Correct answer: $$\frac{45\times3}{1000}$$
$$\frac{45\times3}{10000}$$
Correct answer: $$\frac{45\times3}{10^3}$$
Correct answer: $$\frac{135}{10^3}$$